Communications of the
Korean Mathematical Society CKMS

Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; {\mathbb Q})\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; {\mathbb Q})=0$ or if $\pi_{2n}(X^{2n}) \otimes {\mathbb Q}=0$ for all $n$, then $X$ is an $F_{0}$-space.

Keywords: Rationally elliptic space, Sullivan model, Quillen model, Whitehead exact sequence, $F_{0}$-space

MSC numbers: 55P62